Apparatus for generating a function tape



Dec. 19, 1961 G. MUFFLY APPARATUS FOR GENERATING A FUNCTION TAPE 3 Sheets-Sheet 1 Original Filed Dec. 3l, 1956 Qnnunuungnun nnnnunuupunuuljnuununnuqn 25" IMQ/H595 V ff/7 307 Alarm CdM/iff) fag. J

Dec. 19, 1961 G. MUFFLY APPARATUS FOR GENERATING A FUNCTION TAPE 3 Sheets-Sheet? Original Filed Deo. 3l, 1956 IN VEN TOR. GAQV All/F152 y Arran/Afr Dec. 19, 1961 G. MUFFLY 3,013,857

APPARATUS FOR GENERATING A FUNCTION TAPE Original Filed Deo. 3l, 1956 5 Sheets-Sheet 5 D/SPL ACEA/ENT J #4R/ABLE 510550 DRIVE United States Patent Oiiice 3,913,857 Patented Dec. 19, 1961 3,913,857 APPARATUS FOR GENERATING A FUNCTION TAPE Gary Mutily, Oakmont, Pa., assignor to Gulf Research & Development Company, Pittsburgh, Pa., a corporation of Delaware Original application Dec. 31, 1955, Ser. No. 631,726. Divided and this application July 8, 1958, Ser. No; 749,575

4 Claims. (Cl. 346-74) The invention of this application concerns apparatus for generating' a function tape and more particularly 'pertains to a novel apparatus for recording on a magnetizable record tape signals from which the desired function can vsubsequently be reproduced by the use of an appropriate function unit.

rThis application is a division of my copending application Serial No. 631,726, filed December 3l, 1956, now U. S. Patent 2,948,467, and is assigned to the same assignee as said application.

The apparatus of this invention comprises a novel type of function-tape generator in which the tape motion is linearly related to the input, i.e. the independent variable, and is also linearly related' to the output, i.e. the dependent variable, by including in the tape-moving means a differential type of motion combining and summing mechanism so that the tape motion L is given by the relation l `which the drawings form a part, and in which:

FIGURE l is a schematic diagram of the function unit on which the function tape generated by this invention is tothe used;

FEGURE 2 shows a diagrammatical representation of the magnetized portions of the function tape generated by this invention;

FIGURE 3 is a diagrammatical representation of a portion of the gearing employed in the apparatus; and

FIGURE 4 is a block diagram of the apparatus of this invention.

This invention comprises apparatus for generating a magnetized record tape on which is recorded any desired function or arbitrary control program which may be subsequently reproduced by the functionunit described and claimed in aforementioned parent application Serial No. 631,726. The apparatus moves the record tape by means of a motion combining and summing mechanism and simultaneously generates two quadrature signals that represent the dependent variable, which signals are recorded on the 'record tape. The output or dependent variable is monitored and through the summing mechanism is added to the input or dependent variable whereby the tape motion is related to both variables as will become evident by the following description of the apparatus. Between the tape drive and the quadrature signal generator there are interposed means whereby the operator may adjust the rate or slope of the function that is recorded by the signals and also means whereby the operator may adjust the displacement or position of the recorded signals in order to accurately match the desired function. The invention is best understood by first describing the function unit in which the tape is to be used, which function unit is described and claimed in the aforementioned parent application Serial No. 631,726.

A simplified embodiment of the invention is'schematically illustrated in v)FIGURE 1, wherein 13 representsan elongated magnetizable record medium having sprocket holes 18 which are engaged by the teeth of sprocket wheel 12. The sprocket 12 is driven by a shaft 11 which connects the sprocket to differential gearing 10. The differential gear 1() is driven by two shafts 8 and 9 arranged so that the motion of shaft 11 is proportional to the sum of two quantities which are respectively proportional to the motions of shafts 8 and 9. Accordingly, if shaft 9 were held fixed the motion of shaft 11 would be proportional to the motion of shaft 8 and the tape 13 would be moved longitudinally by an amount also proportional to the rotation of shaft S. Rotation of shaft 8 is the independent variable which is the input to the function unit. l

The magnetic tape 13 has two magnetized record tracks i?) and rthe manner in which these record tracks are generated will be explained later. The record tracks 19 and 20 are magnetized so that a pair of electromagnetic transducing heads 21 and 22 engaging the tracks will pick up the recorded signals. The track signals are in quadrature and therefore the respective signals picked up by the two heads are out of phase. The structure of the magnetic reproducing heads 21 and 22 and the manner in which the reproducing heads 21 and 22 cooperate with the tracks 19 and 20 is clearly described in my US. Patent 2,832,839. The picked-up signals are respectively fed to two detector-amplifiers 23 and 24 whose output power drives a two-phase synchro-motor 25. The manner in which the amplified signals from the tracks 19 and 2i) are employed to drive the synchro-motor 25 is well known in the art.

The synchro-motor 25 has an output shaft 30 whose rotation represents the dependent variable. The output shaft 3G is also coupled to one of the input shafts 9 of the differential gearing 1Q, such coupling preferably being through gearing 31. The gearing 31 is preferably made reversible and the purpose of the reversing feature will be described later.

Operation of the device of FIGURE 1 is therefore as follows. Rotation of shaft 8 causes corresponding rotation (except as modified lby the differential 10) of shaft 11 which effects longitudinal motion of the tape 13. The signals on tape 13 are then picked up and drive'the synchronous motor 25 whose output appears at shaft 30. The output is also modified by gearing 31 and fed back to the differential 1t). Accordingly the actual motion of tape 13 is proportional to the input rotation 8 plus some factor times the output rotation 30. lt is apparent that if the function recorded on the magnetic tracks 19 and 2t) changes very slowly the tape motion is very nearly proportional to the change of input. On the other hand if the function changes rapidly, then the tape motion is also increased (speeded-up) by an added amount which is proportional to the change of output. By the use of this invention a relatively low tape speed may be employed in the slowly-changing regions of the function, and the apparatus automatically speeds up the tape in the rapidly-changing regions of the function.

FIGURE 2 illustrates diagrammatically the magnetization of the tape 13. The figure shows the tape 13 with sprocket holes 18 and the two magnetic tracks 19 and 2t) as they would look if certain of theirl features could be made visible. The pole pieces and coils of the heads 21 and 22 are indica-ted at the right of the figure. In accordance with the recording system of the aforementioned U.S. Patent 2,832,839, the pole faces of 'the heads are oriented so as to make an angle of about 22 with the direction of motion of the tape 13. When magnetized by means to be explained later, the tracks will have N and S pole areas similar to those indicated on the tracks 19 and 20. FEGURE 2 shows the flux directions in the tracks by means of arrows, and the diagonal `lines 35 perpendicular to these arrows represent the center line of areas containing respectively the indicated N and S mag netic poles. The tracks 19 and 20 pictured in FIGURE 2 show the angular magnetization of the tracks which results from the heads being oriented at an angle in accordance with the teachings of US. Patent 2,832,839. The magnetic record pictured is one of rapidly-changing wavelength. Also shown in the phase displacement of 90 (or 1A'. wavelength) between the related waves on tracks 19 and 20. rI`hc waves as they would be reproduced are drawn in the lower part of FIGURE 2, wave 33 corresponding to the signal or ux from track 19, and wave 34 corresponding to the signal or iiux from track 20. When, as the tape 13 moves, one of the lines 35 is centered over the air gap of the associated head, both pole tips of the head are adjacent to tape areas of like polarity and no flux circulates around the core of the magnetic head. (At this point the tape magnetization is zero and reverses direction.) However, when the air gap iscentered midway between two lines 35, the pole tips of the head are in contact with tape areas of unlike polarity and the linx through the core is a maximum which results in maximum response from the head. (At this point the tape is magnetized most strongly.) The response amplitude is pictured in curves 33 and 34 for the respective heads 19 and 2G when traversed by tape 13. 1t is desirable that the recorded sine waves be reproduced with reasonably good wave form and that they are everywhere about 90 apart in phase so that the output motor (25, FIGURE l) will run smoothly.

FIGURE 3 illustrates a physical embodiment of the apparatus of FIGURE l. A differential gearing is indicated generally by 10. The spider 76 of the differential is pinned to the shaft 8 which is the input shaft of the function unit. The spider 7h carries the customary planet gears 71 and 72 which mesh with gears 73 and 74. The gears 73 and 74 are both free to rotate on shaft 8. Gear 73 has fastened to it a spur gear 75 which meshes with gear 76 fastened to shaft 11. Gear 74 has fastened to it a spur gear 77 which is driven through spur gear 78, the latter being fastened to an intermediate shaft 90. Intermediate shaft 96 carries a reverse-gear assembly comprising two similar bevel gears 91 and 92 both of which are fastened to a sliding bushing 93 which engages the intermediate shaft 90 by means of splines or a pin and slot as shown. The gears 91 and 92 are so spaced on the bushing 93 that only one or the other of the gears 91 and 92 can mesh with the bevel gear 94 driven by the shaft 30 of a synchro-motor 25. The position of a control arm 95 determines which of the gears 91 or 92 meshes with the motor gear 94, and a tension spring 96 acting on the arm normally holds gear 91 in mesh so as to provide drive in a directional relationship which may be called normal. Under certain conditions which will become evident later, this directional relationship is reversed. This is accomplished by a solenoid 97 energized by battery 117 and under control of contacts 116. Where the directional relationship is to be reversed, some characteristic of the tape is changed, for example its width as illustrated at 113. Whenever the roller 114 contacts the narrower part 113 of the tape 13, the contacts 116 close and the resulting energization of solenoid 97 overcomes the pull of spring 95 to move the control arm 95, thereby shifting the gears 91 and 92 so that gear 92 meshes with 94 thus reversing the relative rotations of shafts 30 and 90.

The synchro-motor 2S has a polarized rotor whose polarization is effected either by a built-in permanent magnet or by energizing a wound rotor with D.-C. The stator of synchro-motor 25 has a two-phase winding whose phase coils `are respectively energized by the amplitied tape signals. The synchro-motor 25 acts as a synchro-repeater, but its operation is somewhat different from that of the common type of A.C. operated synchrorepeater. The synchro-motor 25 drives the output shaft 42 through gears 79 and 80 or alternatively the motor shaft 30 itself may be used as the output.

It is apparent that if gear 74 (or 77) is held stationary then the gear 73 (and 75) will rotate through twice the angle of input shaft S. I-f gear 74 (and 77) is also rotated, then the rotation of gear 73 (and 75) will be proportional to the algebraic sum of two quantities which are respectively proportional to the motions of shaft 8 and gear 77.

The shaft 11 drives the sprocket 12 which meshes with the perforations 18 in magnetic record tape 13. In the figure the sprocket is shown underneath the tape. The magnetic transducing heads 21 and 22 also shown underneath the tape are shown set at an angle with respect to the motion of the tape in accordance with the teachings of aforementioned US. Patent 2,832,839. The heads Z1 and 22 are A.C. excited and are connected to an electronic oscillator and a pair of detector-amplifiers (indicated collectively by 26) from whose output the synchomotor 2S is driven.

The normal directions of motion of the various parts are as shown by means of arrows in FGURE 3 when the independent and the dependent variables are both increasing. A clockwise rotation of input shaft 8 effects clockwise rotation of the spider 76 which in turn effects clockwise rotation of gear 73 (if gear 74 were held) and thus effects counterclockwise rotation of shaft 11. The tape 13 is thus moved toward the left in FIGURE 3. The electrical connections to synchro-motor 25 are such as to effect counterclockwise rotation of gear 94 under normal conditions (contacts 116 open), so that gear 94 meshes with gear 93 and effects clockwise rotation of shaft 90 when the dependent variable is increasing. Obviously these motions reverse when the input is reversed. The machine will run in either direction.

The abo-ve directions (or the reverse of all of them) may be considered normal and are those which occur when the roller rides on wide tape with contacts 116 open. Under certain conditions to be explained later the relative rotations of shafts 30 and 90 is reversed for a special purpose.

Through the gears 94, 93, shaft and gear 78 the counterclockwise rotation of the motor shaft .'50 causes the differential gear 74 (and 77) to rotate counterclockwise in proportion to the output rotation. This motion of gear 74 feeds back additively to the motion of input shaft 8 so that the total rotation of gear 73 (hence also shaft 11) is more than it would have been if gear 74 had not moved. Therefore the rate of gears 75 and 76 may be so coordinated with the number of teeth on sprocket 12, that for a stationary or very slowly-moving output (with respect to a unit change of input) the tape speed is a convenient value, and upon reaching a place in the range of the recorded function Vwhere the output moves rapidly (with respect to a unit change of input) the shaft 11 will be speeded up, whereupon the tape will be moved faster. This spreads out the signal impulses on the tape where they would otherwise be tightly hunched. The expansion increases the accuracy or resolution as well as the reliability of the function unit in this region over what would be obtained without the feedback. The apparatus thereby permits using relatively shorter wavelength tape signals for the slowly-changing regions of the function and it automatically expands the tape signals for the more rapidly-changing regions of the function, thereby maintaining a high degree of accuracy throughout the tape but without need for an unduly long tape. The apparatus in this manner distributes the changes in the function more evenly over the entire tape and thereby uses the tape more efficiently from the standpoint of accuracy.

Inasrnuch as the motion which is coupled from the output back to the input is a form of mechanical feedback, it is necessary that the apparatus and the functions for which it is to be used be of such form that stability shall be maintained. VThe stability criterion is most conveniently studied from a mathematical analysis of the tape motion. Referring to FIGURE 1, let z" be the input and f() be the output, Where f represents the functional relationship between input and output. It is of course necessary that both i and f(i) Ibe real (not imaginary) and also that f(z) be single valued for the region of the function over which the apparatus is to be used. Let L be the tape displacement (in inches) for an input value i corresponding to an output )(i). We can then describe the action on the differential as L=Ci-|Kf(i) where C is the amount of tape motion that would be caused by a unit of input if the shaft 9 were clamped, and K is the amount of tape motion that would be caused by a unit of output from shaft 3% if the shaft 8 could be clamped. The constant C is determined by the sprocket 12 dimensions as well as the gear ratio through the differential 1t) from shaft 8 to shaft 11. The constant K is determined by the sprocket 12 dimensions, the gear ratio through the differential 14) from shaft 9 to shaft 11, and the ratio of feedback gearing 31 (FIGURE l).

The rate of change of L can be determined by differentiating the above equation with the result or to run away if dl/a'i becomes infinite. it is apparent that if C and K are always positive values, dI/d is always finite and not Zero so long as df(i)/d remains finite and positive. The quantity df()/di is the slope of the recorded function. Therefore the apparatus as described will be` stable over all values of i for which the slope of ythe curve of f(z') (output) plotted against z' (input) is positive and not infinite.

The value dL/ di is still nite and positive when df(i) /d is negative provided its absolute value is less than C/K. An equivalent way of expressing this is that the algebraic value of must be greater (i.e. more positive) than C multiplied by (-1).

For regions of the curve of f(z') where the slope is negative, the action of the apparatus as so-far described is to accentuate non-linearity rather than to alleviate it, and therefore its application in this region is limited to special curves of which the greater part of the useful region of the function has a positive slope and only a relatively small region of limited negative slope is to be included. Of course the values of C and K may be made such as to accommodate as much of the negative-slope region as is desired.

In the event that it is necessary to work with a function that has both positive and negative slopes of high value the above limitation arising from stability considerations may be circumvented by arranging the gearing 31 to be reversed whenever the slope of the function reverses. By such means the algebraic sign of K is changed at the appropriate point so that operation is always in a stable region. One Way in which the reversal is automatic-ally accomplished is illustrated diagrammatically in FIGURE l. The tape 13. is made somewhat narrower 6 as illustrated at 113 (FIGURE 1) over the region where the .slope of the recorded function L@ dt is negative. A rol-ler 114 rides against the edge of the tape and is held in contact with the edge of the tape by spring 115. The roller 114 actuates a contact 116 which is so arranged that the contact is open over the region where the tape 13 is of normal width, and the Contact 114 closes when the roller rides on the narrower tape at 113. Closure of the contacts 116 completes an lelectric circuit from battery 117 to a solenoid (not shown in FIGURE 1) in the reversible gear unit 31 and reverses the direction of the feedback gearing. By this means the apparatus is made stable for all values of df(i)/di that are not infinite. The reversal of gearing 31 is easily accomplished because it takes place at a point where df(z')/di is zero (i.e. changing from positive to negative) which means that the output f() is going through a maximum or a minimum and hence the shafts 30 and 9 are at a standstill.

FIGURE 3 illustrates a physical embodiment of one type of reversible gearing and this has already been described. In FIGURE 3, closure of contacts 116 effects energization of solenoid 97 which reverses the relative Irotation of shafts 30 and 90 without however changing their speed ratio. In this manner the sign of the feedback constant K is automatically changed so that the term is always positive whereby the apparatus is always maintained in the region of stable operation.

The method and apparatus employed to record `a given function on the tape may now be described with reference to FIGURE 4.

The apparatus for making the function tape is shown in FIGURE 4 in block diagram form, the tape 13 being shown longitudinally positioned by rotation of the sprocket 12 fastened to shaft 11. The input shaft 8 is turned by a crank 38 or other convenient means and drives the shaft 11 through the differential gearing 10. The tape is stored wound on the drums 14 and 15 which are respectively driven by torque motors (not shown) to maintain the tape 13 wound up and taut as it traverses the magnet-ic recording heads Z1 and 22 indicated diagrammatically only. An input counter 36 is geared to the input shaft 8 with gears 37 of `appropriate ratio so that the counter 36 reads the independent (input) variable to the desired precision. The shaft 11 is also connected to rotate a synchrgenerator 39 through a continuously-adjustabie variable-speed drive 40 having `adjustment knob 45, and through a differential 41 whose third shaft has an adjustment knob 46. Rotation of shaft 11 is thus converted into rotation of shaft 43 with the driving ratio under the control of rate kno-b 45 which is preferably calibrated. The shaft 43 drives shaft 44 through a differential gearing 41 so that additional displacement may be added or subtracted to the motion in passing through the differential, the displacement added or subtracted being introduced by turning displacement knob 46. The units 40 and i1 are weil known mechanical devices and they should be well constructed Without back- 4lash or other mechanical defects. Unit 40 may be a balland-disk drive and unit 41 may comprise planetary type gearing. By these means the shaft 44 is rotated at a predetermined ratio with respect to shaft 11, but the operato-r may make adiustmcnts in the ratio by adjusting rate knob 45 and the operator may also introduce small displacements by turning displacement knob 46.

rThe synchro-generator 39 is of a type well known to the art and is sometimes called a synchro-transmitter. Its primary is excited at a fixed A..C. voltage from A.C. source .47. its secondary has two windings in quadrature -and these deliver voltages which are proportional to the primary voltage multiplied respectively by the sine and cosine of the angular position of the rotatable member (usually the primary) which is mechanically connected to shaft 44. The secondary voltages are delivered on leads 48 and 49 respectively and fed into phase-sensitive rectifiers S and 51 of known type. The rectiiiers 50 and 51 are identical and both are excited (sensitized) by a reference voltage from the A.C. source 47 as indicated by lead 52. The voltages obtained from the respective rectiiiers at points 53 and 54 therefore have polarity and instantaneous values which are proportional respectively to the sine and cosine of the angular position of shaft 44. The voltages at 53 and 54 reverse in polarity when the sine and cosine change sign. Furthermore, the values of the voltages remain fixed (like a D.C.) so long as the shaft 44 remains in a Xed angular position, and the voltages at 53 and 54 change only when the angular position of shaft 44 changes. The circuit comprising A.C. source 47, synchro-generator 39, and the phase-sensitive rectiers 50 and 51 are the means for obtaining such sine and cosine voltages, and it is within the purview of this -invention to employ other known equivalent means which produce such sine and cosine voltages in response to the angular position of a shaft (44).

The sine and cosine voltages delivered at points 53 and 54 are recorded on the tape 13 by means of the two magnetic heads 21 and 22 engaging the respective tracks 19 and 20. For high recording fidelity a high-frequency bias from oscillator 55 may be introduced through condensers 56 and 57 and resistors 58 and 59 as is customary in the magnetic-recording art, the bias frequency being sufciently high so that it does not record as such on the tracks but merely serves to prevent distortion of the wave shapes. The magnetic tracks 19 and 20 are thus magnetized and each 360 rotation of rotatable transformer 39 will produce on the tape 13 a pair of sinusoidal waves each one cycle long but with 9G phase difference between them.

The voltages at points 53 and 54 are respectively amplified by the conventional amplifiers 60 and 61 which are capable of amplifying D.C. signals as well as very low frequencies. The amplified signals are then fed to the quadrature coils of a Z-phase synchro-repeater or synchro-motor which is in all respects similar to the `rnotor 25 of FIGURES 1 and 3. It is convenient to combine the apparatus of FIGURES 3 and 4 into a single apparatus in which event the synchrornotor 25 of FIG- URE 4 may in fact be the same as motor 25 of FIGURE 3, suitable switching means being provided so that the motor performs its proper function at the proper time. Rotation of motor 25 is proportional to the value of the dependent variable, and the latter may be indicated by a counter 82 connected to the motor by gearing (79 and Sit of FIGURE 3) to provide the desired precision.

The shaft of the synchro-motor 25 is also connected through the feedback gearing 3f. to shaft 9 which enters the differential 10. The rotations are arranged so that whenever the slope of the recorded function df(z')/di is positive, a positive rotation of shaft 30 would effect positive rotation of shaft 11 if the input shaft 8 were held iixed. In this manner the rotation of shaft 11 and the resulting motion of tape 13 is proportional to the sum of two quantities which are respectively proportional to the motions of shafts 8 and 9.

A switch 64 is provided in the recording circuit so that the operator is able to monitor the functional relationship between the counters 36 and S2 with switch 64 open prior to actual recording. The desired relationship is obtained by adjusting the rate knob 45 and the knob 46. When the relationship is as desired, the operator can close switch 64 and record that part of the tape covering the range of values over which he has obtained a t. If the slope of the function changes (as it will in general) the operator can adjust the rate knob 45 so as to maintain the correct slope. In this manner the tape 13 may be magnetized a section at a time, each region of the function represented being iirst checked by the operator and the recording made when proper adjustments have been achieved. i

If a mistake is made, the erroneous part of the tape may be erased `by means of the same heads 21 and 22 using known erasing techniques, after which the corrected function is recorded in its place. However, with a little practice an operator can record an entire function with little or no backtracking. Obviously, counter 82 must be capable of indicating errors of inconsequential size so that errors can be detected before they become signilicant. Whenever the least observable change from the desired function takes place, the operator may correct the dependent variable being recorded by turning the displacement knob 46. The displacement knob 46 should never be changed by more than a small fraction of a wavelength at a time, as otherwise the synchro-motor 25 will jump undesirably whenever the discontinuity on the tape is passed during subsequent operation of the unit. A shift of knob 46 corresponding to 11i or 2@ degrees motion of the synchro-motor can be toicrated and the motor will follow smoothly enough. The differential 41 with displacement knob 46 is not essential to the apparatus, but is useful in preventing overadjustment of rate knob 45 when trying to track the desired function. The knob 46 gives a quicker correction with less tendency to overshoot whenever it becomes apparent to the operator that he is drifting from the desired curve.

In the apparatus of FIGURE 4, the automatic reversal of the feedback gearing 31 is manually performed by the operator during the recording process. Since the function being recorded is known to the operator he will from a plot of the function know where the slope df(z') /di changes from positive to negative and vice versa. When a change from positive slope to negative slope occurs, the operator closes switch and when the slope again becomes positive the operator opens switch 120, thus maintaining the switch 120 closed over the negative-slope regions of the function. The switch 121) completes a circuit through battery 121 which actuates the reversing mechanism of the feedback gearing 31 as described in reference to FIG- URE 3. The circuit also actuates a cutter 122 adjacent the edge of the tape 13 so that the cutter 122 cuts the tape to make it Slightly narrower (as at 113 shown in FIG- URES 1 and 3). The part of the tape with reduced width later controls the automatic reversal of the feedback gearing as previously explained.

It should be noted that the signals of record tracks 19 and 20 correspond to the rotation of motor 25 but they do not themselves express the functional relation to the input (rotation of shaft 8) because the latter is modified by the feedback introduced by rotation of shaft 9.

The apparatus of this invention has been described using a two-phase system, but three or even more phases can be used if desired. In generating a tape with three tracks the synchro-generator 39 -of FIGURE 4 will have three secondary windings which will deliver voltages 120 apart. These will be separately rectified by means of three phase-sensitive rectifiers and the three component voltages are fed to three recording heads and also monitored by means of a three-phase synchro-motor. Such a three-phase system has the advantage of more accurate synchronization of the output motor with the magnetic tracks, thereby further improving the accuracy of the device.

In the appendant claims the connecting means transmitting motion from one shaft to another are understood to transmit motion from either shaft to the other and in linear proportion such as is effected by common gearing, including also a one-to-one proportionality of motion which alternatively may be effected by a direct connection as is well known.

What I claim as my invention is:

1. Apparatus for generating a function tape comprising an input shaft, an output shaft, an elongate magnetizable record tape, means for longitudinally moving said record tape, a differential motion-combining means having three shafts with motion of the third shaft being proportional to the sum of two quantities which are respectively proportional to the motions of two additive shafts, means transmitting motion from said input shaft to one of said additive shafts, means transmitting motion from said tape-moving means to said third shaft having a rotatable shaft and, electromechanical generating means generating signals representative of vector components of the rotation angle of the shaft thereof, an adjustable ratio transmission connecting said third shaft to the shaft of said generating means, a multiphase synchro-motor having multiphase windings, means electrically connecting said respective motor windings to said generating means, means transmitting motion from said synchro-motor to said output shaft, means transmitting motion from said output shaft to the other of said additive shafts, and transducing means electrically connected to said generating means and magnetically engaging said record tape for magnetically recording said vector component signals on said record tape.

2. Apparatus for generating a function tape comprising an input shaft, an output shaft, an elongate ma gnetizable record tape, means for longitudinally moving said record tape, a differential motion-combining means having three shafts with motion of the third shaft being proportional to the sum of two quantities which are respectively proportional to the motions of two additive shafts, means transmitting motion from said input shaft to one of said additive shafts, means transmitting motion from said tapemoving means to said third shaft, an adjustab`e ratio transmission, a differential gearing, electromechanical generating meanshaving a rotatable shaft and generating signals representative of vector components of the rotation angle of the shaft thereof, means transmitting motion from the shaft of said generating means to said third shaft through said transmission and through said differential gearing whereby extraneous rotations may be introduced into the transmitted motion, a multiphase synchro-motor having multiphase windings, means electrically connecting said respective motor windings to said generating means, means transmitting motion from said synchro-motor to said output shaft, means transmitting motion from said output shaft to the other of said additive shafts, and transducing means electrically connected to said generating means and magnetically engaging said record tape for magneticaly recording said vector component signals on said record tape.

3. Apparatus for generating a function comprising an input shaft, an output shaft, an elongate magnetizable record tape, means for longitudinally moving said record tape, a differential motion-combining means having three shafts with motion of the third shaft being proportional to the sum of two quantities which are respectively proportional to the motions of two additive shafts, means transmitting motion from said input shaft to one of said additive shafts, means transmitting motion from said tapemoving means to said third shaft, electromechanical generating means having a rotatable shaft and generating signals representative of thesine and cosine of the rotation angle of the shaft thereof, an adjustable ratio transmission connecting said third shaft to the shaft of said generating means, a two-phase synchro-motor, means electrical'y transmitting motion from said respective motor windings to said generating means, means transmitting motion from said synchro-motor to said output shaft, means connecting said output shaft to the other of said additive shafts, and two transducing means electrically connected to said generating means and magnetically engaging said record tape for magnetically recording said sine and cosine signals on said record tape.

4. Apparatus for generating a function tape comprising an input shaft, an output shaft, an elongate magnetizable record tape, means for longitudinally moving said record tape, a differential motion-combining means having three shafts with motion of the third shaft being proportional to the sum of two quantities which are respectively proportional to the motions of two additive shafts, means transmitting motion from said input shaft to one of said additive shafts, means transmitting motion from said tapemoving means to said third shaft, an adjustable raito transmission, a differential gearing, electromechanical generating means having a rotatable'shaft and generating signals representative of vector components of the rotation angle of the shaft thereof, means transmitting motion from the shaft of said generating means to said third shaft through said transmission and through said differential gearing whereby extraneous rotations may be introduced into the transmitted motion, a multiphase synchrorotor having multiphase windings, means electrically connecting said respective motor windings to said generating means, means transmitting motion from said synchromotor to said output shaft, reversible means transmitting motion from said output shaft to the other of said additive shafts, means for reversing said reversible means whenever the slope ofthe functional relationship is negative, and transducing means electrically connected to said generating means and magnetically engaging said record tape for magnetically recording said vector component signals on said record tape.

References Cited in the file of this patent UNITED STATES PATENTS 2,496,103 Neufeld Ian. 31, 1950 2,798,998 Marks July 9, 1957 2,816,257 Burdorf Dec. l0, 1957 2,843,446 Pettus et al. July l5, 1958 UNITED STATES PATENT OFFICE lCERTIIFICMIE OF CORRECTION Patent No@ 3Ol3857 December 19g i961 Gary Muffly.

It is hereby certified that error appears in the above numbered petent requiring correction and that the said Letters Patent should read as corrected below.

Column 9I lines 9 and lOI strike out "having" a rotatable' shaft andi" and insert the same after Nmeans in line 10V same column; same column 9S7 line 5lU after 'fnnction" ineert tape --5 column lOI line llV for Utminomilttinq motion fromm reed connecting line 14V :for 'oonneeting" read transmite ting motion from --5 same Column 10V line 28XI for "'raito" read ratio ws.,

Signed and sealed this ist day of May 1962.,-

(SEAL) Attest:

E TEST wt SWIDEE DAVID L LADD Attesting Officer Commissioner of Patents UNITED STATES PATENT OFFICE .CERTIFICATE 0F CORRECTIGN Patent E@ev 3o13e5? neember 19 1961 Gary Mnffly It is hereby certified that error appears in the abo-ve numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 9V lines 9 and 10X7 strike ont uhai/fing a rotatable' .shaft end' and insert the same after meansvs in line 10 same column; Same column 9 line '51U after V'fnnction" insert tape column lOI line l1u for transmitting motion fromn read connecting mg line 14h for IWaerme@ting*u reed t,lmantssrnitel ting motion from --g same Column l()v line 28 for Taito Signed and sealed this lst dey of Mey 1962Y (SEAL) Attest:

DAVID L. LADD Commissioner of Patents EEST SWTDEE Attesting Officer 

